I may be the least experienced at this game but I know from playing WoW and FFXIV that a lot of times you just don't know all thing things available for end-game. With that said, feel free to recommend, add, or remove.
Guild Events - Check the Guilded Calendar or even better, work with your squad and create your own!
Legendary - Go through the main story on all 4 classes on both Republic and Imperial side for a special frame on your portrait (Flair) and title. You will also unlock all of your Heroic Moment abilities and get a shiny Guild Badge!
Gearing Up - get all of your toons to max gear and the best amplifiers. This includes getting bonus gear sets.
Operations and Flashpoints - Master level!
Warzones - PvP and you get commendations you can use for special gear!
World PvP - enjoy fighting
Ranked Warzones - Show off to the guild by getting ranked and working your way to #1
Galactic Starfighter - Pvp but with fighters. An amazing aspect of SWTOR that is completely different than your normal MMORPG.
Special Events - Things like Bounty Contract Week or Nightlife event (You can find info on these on the blog https://www.imperialarmy.org/blog )
Crafting - contribute to the guild or make some money selling on the GTN
Achievements - are you a completionist? Show off your hard work!
Holocrons - Increase your stats across your character's for maximum power!
Roleplaying (RP) - Just ask Nora and Dee, there are so many great things to do!
Galactic Strongholds - You can decorate, show off, and even set up a Hutta ball match!
Great post bare!
I'll add somethings a little more specific too, most of these fall under "achievements"
Unlock all the companions available to your character via Star Fortresses and Alliance Alerts
Complete the Space Missions on your Ship's main console
Complete the Bonus Series Missions after completing the Planetary Missions for each Planet
Max out Reputations and unlock unique customizations, recipies, and mounts
Hunt down the Secret Pets
Complete the Seeker Droid Missions
Unlock HK-51